Math 2 Quiz: Comparing Model Fits
14 questions · exam conditions
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Comparing Model FitsQuestion 1 of 14

A marketing team analyzed customer satisfaction scores against product price using linear and quadratic models. The linear model shows satisfaction decreasing as price increases (β1=−0.3\beta_1 = -0.3, R2=0.65R^2 = 0.65). The quadratic model shows satisfaction initially increasing with price then decreasing (R2=0.81R^2 = 0.81), suggesting customers associate higher prices with quality up to a point. Both models pass significance tests. Which model comparison is most justified?

The linear model is better because customers always prefer lower prices, making the negative relationship more intuitively correct than quadratic complexity.
The linear model is better because it provides clearer pricing guidance and avoids the complexity of identifying optimal price points.
The quadratic model is better because it captures the psychological pricing effect where moderate price increases signal quality before becoming prohibitive.
The quadratic model is better because higher R2R^2 indicates superior statistical performance regardless of the underlying consumer psychology.
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Math 2 Quiz

Math 2 Quiz: Comparing Model Fits

Practice Comparing Model Fits in Math 2 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Comparing Model Fits, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 2.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A marketing team analyzed customer satisfaction scores against product price using linear and quadratic models. The linear model shows satisfaction decreasing as price increases (β1=−0.3\beta_1 = -0.3, R2=0.65R^2 = 0.65). The quadratic model shows satisfaction initially increasing with price then decreasing (R2=0.81R^2 = 0.81), suggesting customers associate higher prices with quality up to a point. Both models pass significance tests. Which model comparison is most justified?

  1. The linear model is better because customers always prefer lower prices, making the negative relationship more intuitively correct than quadratic complexity.
  2. The linear model is better because it provides clearer pricing guidance and avoids the complexity of identifying optimal price points.
  3. The quadratic model is better because it captures the psychological pricing effect where moderate price increases signal quality before becoming prohibitive. (correct answer)
  4. The quadratic model is better because higher R2R^2 indicates superior statistical performance regardless of the underlying consumer psychology.
Explanation: When comparing statistical models, you need to balance three key factors: statistical fit, theoretical justification, and practical interpretability. This question tests whether you can prioritize these appropriately in a real-world context. The quadratic model (Answer C) is superior because it captures a well-documented psychological pricing phenomenon. Consumers often use price as a quality signal, creating an inverted U-shaped relationship where satisfaction initially rises with price (quality perception) before falling due to affordability concerns. The higher R2=0.81R^2 = 0.81 confirms this model explains more variance in the data, and the theoretical foundation makes this improvement meaningful, not just statistical noise. Answer A incorrectly assumes customers always prefer lower prices, ignoring quality perceptions. This oversimplifies consumer psychology and contradicts empirical evidence of premium pricing success. Answer B prioritizes simplicity over accuracy—while linear models are easier to interpret, using a worse-fitting model for convenience sacrifices valuable insights about optimal pricing. Answer D commits the opposite error of focusing solely on R2R^2 without considering whether the improvement reflects genuine underlying relationships versus overfitting. The key insight is that higher R2R^2 alone doesn't justify model selection, but when combined with strong theoretical support (as here), it indicates the more complex model captures real patterns rather than random variation. Study tip: In model comparison questions, always ask yourself: Does the better-fitting model align with established theory or logic? Statistical superiority plus theoretical justification typically trumps simplicity, while statistical superiority alone may indicate overfitting.

Question 2

A quality control engineer compared linear and quadratic models for predicting product defect rates based on production speed. The linear model predicts defects increase steadily with speed. The quadratic model shows defects decrease initially (as workers get into rhythm) then increase at high speeds (as workers make errors). Both models have similar predictive accuracy on the training data. Considering manufacturing psychology and process optimization, which evaluation is most sound?

  1. The linear model is better because it provides simpler guidelines for production management and avoids overcomplicating the relationship.
  2. The linear model is better because it assumes workers maintain consistent performance regardless of speed, which is easier to plan for.
  3. Both models are equivalent since they have similar accuracy and the choice depends on management preference for simplicity versus complexity.
  4. The quadratic model is better because it reflects realistic human performance patterns and could identify optimal production speeds. (correct answer)
Explanation: When evaluating statistical models in real-world applications, accuracy alone isn't sufficient—you must consider whether the model reflects the underlying process and provides actionable insights for decision-making. The quadratic model (Answer D) is superior because it captures realistic human performance patterns that manufacturing psychology supports. Workers typically need time to reach optimal rhythm at moderate speeds, explaining the initial decrease in defects. At excessive speeds, cognitive overload and motor errors increase, causing defects to rise again. This creates the U-shaped curve that quadratic models represent. Crucially, this model can identify an optimal production speed that minimizes defects—invaluable for process optimization. Answer A is flawed because simplicity shouldn't override accuracy when the stakes involve product quality and worker performance. Manufacturing processes aren't inherently simple, and oversimplified models can lead to poor decisions. Answer B incorrectly assumes workers perform consistently regardless of speed, which contradicts established research on human factors in manufacturing. This assumption could lead to setting speeds that maximize errors. Answer C treats the models as equivalent based solely on training accuracy, ignoring the critical factors of interpretability, underlying assumptions, and practical utility. Equal accuracy doesn't mean equal value for decision-making. Study tip: When comparing models with similar accuracy, always consider which one better reflects the underlying process and provides more actionable insights. In applied statistics, the most useful model often incorporates domain knowledge about how the system actually works, not just mathematical fit.

Question 3

A biologist studying bacterial growth fitted both exponential and quadratic models to colony size over time. The exponential model has R2=0.89R^2 = 0.89 but systematically underpredicts at early and late time points. The quadratic model has R2=0.94R^2 = 0.94 with better residuals, but predicts the colony will eventually shrink. Considering that bacterial colonies typically follow exponential growth until resource limitations occur, which evaluation is most sound?

  1. The exponential model is better because it aligns with known biological growth patterns, despite having systematic prediction errors.
  2. The quadratic model is better because it has superior statistical performance and the prediction of decline could represent resource limitation.
  3. Neither model is adequate because exponential models can't capture resource limitations while quadratic models don't represent biological reality. (correct answer)
  4. Both models are equally flawed since one ignores statistical evidence while the other ignores biological principles entirely.
Explanation: This question requires recognizing that both models have fundamental limitations for this biological context. Exponential models can't capture the resource limitation phase that bacterial colonies experience, while quadratic models don't represent the biological mechanism of growth followed by plateau/decline. A logistic model would be more appropriate. Choice A ignores that exponential growth doesn't account for resource limits. Choice B incorrectly suggests quadratic decline represents resource limitation. Choice D suggests they're equally valid when both are actually inadequate.

Question 4

A sports scientist studying the relationship between training intensity and athletic performance found that a linear model predicts steady improvement with increased intensity (R2=0.76R^2 = 0.76). A quadratic model suggests performance peaks at moderate intensity then declines with overtraining (R2=0.84R^2 = 0.84). The quadratic model aligns with overtraining syndrome research. However, the linear model's residuals show no obvious patterns. Which model evaluation is most appropriate?

  1. The quadratic model is better because it reflects sports science understanding of overtraining syndrome and has superior statistical fit. (correct answer)
  2. The linear model is better because random residuals indicate good model fit, even though the R2R^2 is lower than the quadratic model.
  3. The models are equivalent because both show adequate statistical performance and the choice depends on coaching philosophy about training intensity.
  4. The linear model is better because it encourages athletes to train harder, which builds mental toughness and competitive advantage.
Explanation: When evaluating competing statistical models, you need to balance three key factors: statistical fit (like R2R^2), theoretical soundness, and residual patterns. This question tests your ability to weigh these considerations appropriately. The quadratic model is superior because it excels in two of the three evaluation criteria. First, it has better statistical fit with R2=0.84R^2 = 0.84 versus R2=0.76R^2 = 0.76 for the linear model, meaning it explains 84% of the variance compared to 76%. Second, and crucially, it aligns with established sports science theory about overtraining syndrome—the well-documented phenomenon where excessive training intensity actually decreases performance. This theoretical grounding makes the quadratic model's inverted-U shape (performance peaks then declines) scientifically credible. Looking at the wrong answers: B incorrectly prioritizes residual patterns over both statistical fit and theoretical validity. While random residuals are good, they don't outweigh an 8-point R2R^2 difference and theoretical mismatch. C wrongly suggests the models are equivalent when one clearly has superior fit and theoretical support—model selection isn't just about coaching philosophy. D is completely inappropriate because statistical model choice should never be based on motivational considerations rather than scientific evidence. Study tip: In model comparison questions, remember that the best model typically combines strong statistical performance with theoretical justification. A model that contradicts established scientific understanding should be viewed skeptically, even if it has decent fit statistics.

Question 5

A researcher collected data on the height of a plant over time and fitted both linear and quadratic models. The linear model has R2=0.78R^2 = 0.78 and residuals that show a clear curved pattern. The quadratic model has R2=0.91R^2 = 0.91 and residuals that appear randomly scattered. However, the quadratic model predicts the plant will reach a maximum height and then decrease. Which statement best evaluates these models?

  1. The linear model is better because it makes more biological sense, even though it has lower R2R^2 and patterned residuals.
  2. The quadratic model is better because it has higher R2R^2 and better residuals, despite the unrealistic biological prediction.
  3. The models are equally valid since both have reasonably high R2R^2 values and different strengths in different areas.
  4. Neither model is appropriate since one lacks biological realism and the other shows clear patterns in residuals. (correct answer)
Explanation: A good model must satisfy both statistical criteria (high R², random residuals) and contextual appropriateness. The linear model fails statistically due to patterned residuals indicating poor fit. The quadratic model fails conceptually because plants don't typically decrease in height over time. Both models have fundamental flaws that make them inappropriate. Choice A ignores the serious statistical problems with the linear model. Choice B ignores the biological implausibility. Choice C fails to recognize that both models have critical flaws.

Question 6

A data analyst compared linear and quadratic models for predicting house prices based on square footage. Both models have similar R2R^2 values (0.84 vs 0.86), but the quadratic model's coefficient for the squared term is negative, suggesting that very large houses decrease in value per square foot. The linear model predicts consistent price increases. Given that extremely large houses often have unique market challenges, how should these models be evaluated?

  1. Choose the linear model because it has simpler interpretation and the R2R^2 difference is negligible for practical purposes.
  2. Choose the quadratic model because it reflects real market dynamics where extremely large homes face pricing challenges per square foot. (correct answer)
  3. Choose based on prediction accuracy alone since both models explain similar amounts of variance in the housing market.
  4. Reject both models since the R2R^2 values are too similar to make a meaningful distinction between their predictive capabilities.
Explanation: The quadratic model's negative coefficient for the squared term actually captures a realistic market phenomenon - very large houses often have lower price per square foot due to limited buyer pool, maintenance costs, and market dynamics. This contextual realism, combined with slightly better fit, makes it superior. Choice A ignores important contextual information. Choice C focuses only on statistical measures while ignoring model interpretation. Choice D incorrectly suggests that similar R² values mean both models should be rejected.

Question 7

A environmental scientist compared linear and quadratic models for predicting plant growth rate based on soil nitrogen concentration. The linear model shows consistent growth increase with nitrogen. The quadratic model shows growth increasing then decreasing, suggesting nitrogen toxicity at high levels. Cross-validation shows similar prediction errors for both models on new data. Given plant physiology and the principle of limiting factors, which model assessment is most sound?

  1. The quadratic model is better because it incorporates the biological reality of nutrient toxicity that occurs at excessive concentration levels. (correct answer)
  2. The linear model is better because equal cross-validation performance indicates both models generalize equally well to new situations.
  3. Both models are equivalent since cross-validation is the most important criterion for model selection in scientific applications.
  4. The linear model is better because it provides simpler fertilization guidelines and avoids the complexity of determining optimal nutrient ranges.
Explanation: When evaluating scientific models, you need to balance statistical performance with biological plausibility. While cross-validation measures how well models predict new data, it's only one criterion for model selection in scientific contexts. The quadratic model captures a fundamental biological principle: the law of limiting factors. Essential nutrients like nitrogen initially promote growth, but at excessive concentrations become toxic. This creates the characteristic inverted-U relationship where growth increases to an optimum point, then declines. This pattern is well-documented in plant physiology and reflects real biological processes like nutrient burn and osmotic stress. Option A is correct because it recognizes that biological realism should guide model choice when statistical performance is equivalent. The quadratic model's ability to capture nutrient toxicity makes it more scientifically valuable despite similar cross-validation results. Option B incorrectly assumes that equal cross-validation performance makes models equivalent for scientific purposes. Statistical performance alone doesn't determine the best scientific model. Option C makes the same error as B, treating cross-validation as the sole criterion. In science, models must also align with known biological mechanisms to provide meaningful insights. Option D focuses on practical simplicity but ignores scientific accuracy. Simple fertilization guidelines based on an incorrect model could lead to over-fertilization and crop damage, making this approach counterproductive. Remember: In scientific modeling, when statistical performance is similar, choose the model that better reflects the underlying biological or physical processes. Domain knowledge should inform model selection, not just statistical metrics.

Question 8

A psychologist studies reaction time versus age. The linear model shows residuals that increase in variance with fitted values and R2=0.58R^2 = 0.58. The quadratic model shows constant variance residuals and R2=0.79R^2 = 0.79. The researcher notes that both models predict reasonable reaction times across the age range studied (20-70 years), but the quadratic model suggests reaction times decrease slightly from age 20-30 before increasing. Which evaluation is most appropriate?

  1. Choose the linear model because increasing reaction time with age is more consistent with psychological research
  2. Choose the linear model because non-constant variance in residuals indicates the quadratic model violates assumptions
  3. Choose the quadratic model because it better satisfies regression assumptions and provides superior fit to the data (correct answer)
  4. Choose the quadratic model because higher R2R^2 values always indicate more accurate models for prediction purposes
Explanation: When evaluating regression models, you need to balance two critical factors: how well the model fits the assumptions of linear regression and how well it explains the data. Both matter, but assumption violations can make your results unreliable regardless of fit statistics. The quadratic model is superior here because it satisfies the key regression assumption of constant variance (homoscedasticity) while also explaining more variance in the data (R2=0.79R^2 = 0.79 vs 0.580.58). The linear model's increasing variance with fitted values (heteroscedasticity) violates a fundamental assumption, making its statistical inferences questionable. When you have both better assumptions compliance AND better fit, the choice is clear. Let's examine why the other options miss the mark: A) focuses only on theoretical expectations rather than statistical evidence. While psychological theory matters, you can't ignore what the data actually shows when it's statistically sound. B) reverses which model has the variance problem. The linear model shows non-constant variance, not the quadratic model. The quadratic model actually has constant variance, satisfying the assumption. D) oversimplifies model selection by claiming higher R2R^2 always means better prediction. While R2R^2 is important, it must be considered alongside assumption compliance and model appropriateness. Remember: Good model selection requires examining both statistical assumptions and goodness of fit together. A model that violates assumptions may give misleading results even if it has decent R2R^2, while a model satisfying assumptions with better fit gives you confidence in your conclusions.

Question 9

A chemist models the relationship between catalyst concentration and reaction rate. The linear model gives R2=0.82R^2 = 0.82 with residuals showing no clear pattern. The quadratic model gives R2=0.85R^2 = 0.85 with residuals also showing no clear pattern. However, the quadratic model predicts that reaction rate decreases at very high catalyst concentrations, which contradicts established chemical principles for this reaction type. What is the best approach?

  1. Use the linear model because it aligns with chemical theory and the improvement in R2R^2 is minimal (correct answer)
  2. Use the quadratic model because both models meet assumptions and it has higher explanatory power
  3. Use the quadratic model but acknowledge its theoretical limitations in the interpretation of results
  4. Collect additional data at high concentrations to determine which model better represents reality
Explanation: When evaluating statistical models, you must balance statistical fit with theoretical validity. A higher R2R^2 value doesn't automatically make a model better if it violates fundamental principles of the system being studied. The correct approach is A because scientific modeling requires both statistical adequacy and theoretical coherence. While the quadratic model has a slightly higher R2R^2 (0.85 vs 0.82), this improvement is minimal—only 3 percentage points. More importantly, the quadratic model's prediction that reaction rate decreases at high catalyst concentrations contradicts established chemical theory for this reaction type. The linear model, with R2=0.82R^2 = 0.82 and no pattern in residuals, provides adequate fit while remaining consistent with chemical principles. B is incorrect because higher explanatory power alone doesn't justify using a model that violates domain knowledge. The 3-point R2R^2 improvement is marginal and doesn't outweigh theoretical concerns. C is problematic because knowingly using a theoretically flawed model undermines the scientific validity of your conclusions, even with acknowledgment of limitations. D might seem reasonable, but when you already have models with adequate fit and one aligns with established theory while the other doesn't, additional data collection isn't the priority. The theoretical violation is a fundamental issue, not just an empirical one. Study tip: In model selection, always consider domain expertise alongside statistical measures. A model that fits the data well but contradicts well-established scientific principles should be viewed skeptically, especially when simpler alternatives provide reasonable fit.

Question 10

A sports scientist models the relationship between training intensity and performance improvement. The data shows improvement initially increases with intensity but then plateaus. A linear model yields R2=0.45R^2 = 0.45 with systematic residual patterns. A quadratic model yields R2=0.83R^2 = 0.83 with random residuals. However, the quadratic model predicts that performance improvement becomes negative at very high intensities. How should the scientist proceed?

  1. Reject both models and collect more data since neither adequately represents the plateau behavior described
  2. Use the linear model because negative improvement predictions indicate the quadratic model is fundamentally flawed
  3. Use the quadratic model but limit predictions to the range where it gives reasonable values (correct answer)
  4. Use the quadratic model because it better fits the data, and negative predictions at extreme values are acceptable
Explanation: When you encounter model selection problems in statistics, you need to balance goodness of fit with model validity and practical constraints. The key is recognizing that a model can be useful within its appropriate domain even if it fails outside that range. The quadratic model is superior because it has a much higher R2=0.83R^2 = 0.83 compared to the linear model's R2=0.45R^2 = 0.45, and crucially, it shows random residuals while the linear model has systematic residual patterns. Random residuals indicate the model captures the underlying relationship well, while systematic patterns suggest the linear model is missing important features of the data. The fact that the quadratic model predicts negative improvements at extreme intensities doesn't invalidate it—it simply means you should restrict predictions to the reasonable range where the model applies. Choice A is wrong because the quadratic model does represent plateau behavior through its curved shape, and the high R2R^2 with random residuals shows it fits well. Choice B incorrectly assumes that unrealistic predictions at extremes make the entire model useless—this ignores that most real-world models have limited domains of validity. Choice D is wrong because accepting negative improvement predictions as "acceptable" misses the point that responsible modeling requires acknowledging model limitations. Study tip: In model selection problems, remember that the "best" model isn't always perfect everywhere—look for the model that fits the data well within the relevant range, then apply appropriate constraints to avoid unrealistic extrapolations.

Question 11

A company analyzed the relationship between advertising spend and sales revenue using both linear and quadratic models. The linear model suggests constant returns to advertising investment. The quadratic model has a negative coefficient for the squared term, suggesting diminishing returns, and fits the data better (R2=0.92R^2 = 0.92 vs R2=0.87R^2 = 0.87). However, the quadratic model predicts that extremely high advertising spend would actually decrease sales. How should these models be compared?

  1. The linear model is preferable because constant returns to advertising are more optimistic and encourage continued investment in marketing.
  2. The quadratic model is preferable because diminishing returns to advertising are economically realistic and it fits the data better. (correct answer)
  3. The linear model is preferable because it avoids the unrealistic prediction that advertising could harm sales revenue.
  4. The quadratic model is preferable because higher R2R^2 values always indicate superior models regardless of practical interpretation.
Explanation: Diminishing returns to advertising are well-established in marketing economics - initial advertising has high impact, but additional spending yields progressively smaller benefits. The quadratic model captures this realistic relationship and fits better. The prediction of decreased sales at extreme spending levels, while seemingly unrealistic, actually reflects market saturation or consumer backlash. Choice A uses flawed reasoning about optimism. Choice C focuses on an extreme case that's unlikely to occur in practice. Choice D ignores the importance of model interpretability.

Question 12

A researcher collects data on the relationship between hours of sleep and test scores for 20 students. The linear model yields R2=0.72R^2 = 0.72 with residuals that show a clear curved pattern when plotted against fitted values. A quadratic model for the same data yields R2=0.89R^2 = 0.89 with residuals that appear randomly scattered. However, the researcher notes that the quadratic model predicts negative test scores for students getting less than 3 hours or more than 12 hours of sleep. Which model should be preferred and why?

  1. The quadratic model, because it has a higher R2R^2 value and better residual patterns, indicating superior statistical fit
  2. The linear model, because it provides more realistic predictions across all possible sleep values despite lower statistical measures (correct answer)
  3. The quadratic model, because curved residual patterns in the linear model indicate serious violations of regression assumptions
  4. The linear model, because quadratic models are generally inappropriate for behavioral data like sleep and test performance
Explanation: While the quadratic model has better statistical indicators (higher R² and better residuals), it produces unrealistic predictions (negative test scores) outside the data range. The linear model, despite lower R², provides meaningful predictions across all reasonable input values. Model selection should balance statistical fit with practical interpretability and realistic predictions. Choice A ignores the prediction issues. Choice C overstates the residual problem. Choice D makes an unfounded generalization about quadratic models.

Question 13

A biologist models the relationship between temperature (°C) and enzyme activity. The linear model shows random residuals and R2=0.67R^2 = 0.67. The quadratic model shows random residuals and R2=0.94R^2 = 0.94. However, enzyme activity is known to follow a bell-shaped curve in nature, increasing to an optimal temperature then decreasing. The data only covers temperatures from 20°C to 35°C, all showing increasing activity. What is the most appropriate conclusion?

  1. Use the linear model because it adequately fits the observed data range with simpler interpretation and fewer parameters
  2. Use the linear model because quadratic models require the presence of a peak within the observed data range
  3. Use the quadratic model because higher R2R^2 always indicates a superior model regardless of other considerations
  4. Use the quadratic model because it aligns with biological theory and provides significantly better fit to the data (correct answer)
Explanation: When evaluating statistical models, you need to balance multiple factors: goodness of fit, theoretical foundation, and practical considerations. This question tests your ability to weigh these competing priorities in model selection. The quadratic model is superior here for two key reasons. First, it provides a dramatically better fit to the data (R2=0.94R^2 = 0.94 versus R2=0.67R^2 = 0.67), explaining 94% of the variance compared to only 67% for the linear model. Second, and crucially, it aligns with established biological theory that enzyme activity follows a bell-shaped curve with an optimal temperature. Even though the data only shows the increasing portion (20°C to 35°C), the quadratic model can capture this theoretical relationship and provide better predictions, especially for extrapolation. Option A incorrectly prioritizes simplicity over fit quality and theoretical validity. While simpler models are preferable when fits are comparable, a 27-percentage-point improvement in R2R^2 is substantial. Option B makes a false claim that quadratic models require peaks within the observed range—quadratic functions can model portions of curves effectively. Option C is wrong because higher R2R^2 alone doesn't determine model superiority, but when combined with theoretical support and such a large improvement, it becomes compelling. For model selection questions, remember that the best model typically combines good statistical fit with theoretical justification. Don't automatically choose the simplest model when a more complex one offers substantially better fit and aligns with known scientific principles.

Question 14

A meteorologist models the relationship between atmospheric pressure and wind speed during storms. The linear model produces R2=0.66R^2 = 0.66 with residuals that show slight curvature. The quadratic model produces R2=0.78R^2 = 0.78 with randomly distributed residuals. Both models give reasonable predictions within the observed pressure range, but the quadratic model predicts extremely high wind speeds at pressure values outside the observed range. For weather forecasting purposes, which consideration should be prioritized?

  1. The linear model should be used because its predictions remain stable across a wider range of pressure values (correct answer)
  2. The quadratic model should be used because random residuals indicate it better captures the true relationship
  3. The quadratic model should be used because the improvement in R2R^2 represents meaningfully better explanatory power
  4. The linear model should be used because slight curvature in residuals is acceptable when extrapolation reliability is important
Explanation: When evaluating statistical models for practical applications, you need to balance goodness of fit with model reliability and interpretability. This question tests your understanding of when to prioritize extrapolation stability over pure statistical measures. The key insight here is recognizing that weather forecasting inherently requires predictions outside the observed data range. While the quadratic model shows better statistical fit (R2=0.78R^2 = 0.78 vs 0.660.66) and proper residual distribution, its extreme predictions at unobserved pressure values make it unsuitable for forecasting. Linear models provide more stable, reasonable extrapolations because they don't contain the curved terms that can lead to explosive growth outside the data range. Choice A correctly identifies that prediction stability across pressure ranges is crucial for meteorological applications. The linear model's more conservative extrapolation behavior outweighs its slightly lower explanatory power within the observed range. Choice B incorrectly prioritizes residual patterns over practical utility. While random residuals do indicate better model assumptions, this doesn't guarantee reliable extrapolation. Choice C focuses too heavily on the R2R^2 improvement. An increase from 0.660.66 to 0.780.78 represents better fit to existing data, but doesn't address the extrapolation problems that make the model impractical. Choice D mentions the right conclusion but for the wrong reason. Slight curvature in residuals actually suggests model inadequacy, not something that's "acceptable." Study tip: In applied statistics problems, always consider the intended use case. Models with better statistical measures aren't always better for real-world applications—practical constraints like extrapolation reliability often take precedence.